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Classical properties of algebras using a new graph association
(Cornell University, 2017)
We study the relation between algebraic structures and Graph Theory. We have de ned ve di erent weighted digraphs associated to a nite dimensional algebra over a eld in order to tackle important properties of the ...
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3-filiform Leibniz algebras of maximum length
(Springer, 2016)
This work completes the study of the solvable Leibniz algebras, more precisely, it completes the classi cation of the 3- liform Leibniz algebras of maximum length [4]. Moreover, due to the good structure of the algebras ...
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A historical review of the classifications of Lie algebras
(Unión Matemática Argentina, 2013)
The problem of Lie algebras’ classification, in their different varieties, has been dealt with by theory researchers since the early 20th century. This problem has an intrinsically infinite nature since it can be inferred ...
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Leibniz algebras with associated Lie algebras sl_2\dot{+} R (dim R=2)
(Cornell University, 2011)
From the theory of finite dimensional Lie algebras it is known that every finite dimensional Lie algebra is decomposed into a semidirect sum of semisimple subalgebra and solvable radical. Moreover, due to work of ...
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On the description of Leibniz algebras with nilindex n−3
(Akadémiai Kiadó, 2011)
In this paper we present the classification of a subclass of natu- rally graded Leibniz algebras. These n-dimensional Leibniz algebras have the characteristic sequence equal to (n−3, 3). For this purpose we use the ...
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Solvable Leibniz Algebras with Filiform Nilradical
(Springer, 2016)
In this paper we continue the description of solvable Leibniz algebras whose nilradical is a filiform algebra. In fact, solvable Leibniz algebras whose nilradical is a naturally graded filiform Leibniz algebra are described ...
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Quasi-filiform Leibniz algebras of maximum length
(Springer, 2011)
The n-dimensional p-filiform Leibniz algebras of maximum length have already been studied with 0 p 2. For Lie algebras whose nilindex is equal to n − 2 there is only one characteristic sequence, (n − 2, 1, 1), while ...
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Isotopism and isomorphism classes of certain Lie algebras over finite fields
(Springer, 2015)
In the current paper, we study the distribution into isotopism and isomorphism classes of the relevant family FpnFnp of Lie algebras of basis {e1,…,en}{e1,…,en} and nonzero brackets [ei,en]∈⟨e1,…,en−1⟩[ei,en]∈⟨e1,…,en−1⟩ ...
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p-Filiform Leibniz algebras of maximum length
(Elsevier, 2014)
The descriptions (up to isomorphism) of naturally graded p-filiform Leibniz algebras and p-filiform (p 3) Leibniz algebras of maximum length are known. In this paper we study the gradation of maximum length for p-filiform ...
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Solvable Leibniz algebras with NFn⊕ F1m nilradical
(De Gruyter, 2017)
All finite-dimensional solvable Leibniz algebras L, having N = NFn⊕ F1m as the nilradical and the dimension of L equal to n+m+3 (the maximal dimension) are described. NFn and F1m are the null-filiform and naturally graded ...